Solve the Fraction Addition: 3/6 + 3/9 Step-by-Step

Fraction Addition with Different Denominators

Solve the following equation:

36+39= \frac{3}{6}+\frac{3}{9}=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Multiply each fraction by 3 and 2 respectively to find the common denominator
00:07 Make sure to multiply both numerator and denominator
00:19 Calculate the multiplications
00:25 Add with the common denominator
00:29 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

36+39= \frac{3}{6}+\frac{3}{9}=

2

Step-by-step solution

We must first identify the lowest common denominator between 6 and 9.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 6 and 9.

In this case, the common denominator is 18.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 18.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 2

3×36×3+3×29×2=918+618 \frac{3\times3}{6\times3}+\frac{3\times2}{9\times2}=\frac{9}{18}+\frac{6}{18}

Finally we'll combine and obtain the following:

9+618=1518 \frac{9+6}{18}=\frac{15}{18}

3

Final Answer

1518 \frac{15}{18}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find the least common denominator before adding fractions
  • Technique: Convert 36 \frac{3}{6} to 918 \frac{9}{18} and 39 \frac{3}{9} to 618 \frac{6}{18}
  • Check: Simplify the result if possible: 1518=56 \frac{15}{18} = \frac{5}{6}

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 36+39 \frac{3}{6} + \frac{3}{9} as 615 \frac{6}{15} by adding 3+3=6 and 6+9=15! This ignores the fundamental rule that fractions need common denominators. Always find the LCD first, then convert both fractions before adding numerators.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

FAQ

Everything you need to know about this question

How do I find the LCD of 6 and 9?

+

List the multiples of each number: 6: 6, 12, 18, 24... and 9: 9, 18, 27... The first number that appears in both lists is 18, so that's your LCD!

Why can't I just add the fractions as they are?

+

You can only add fractions when they have the same denominator. Think of it like adding different units - you can't add 3 apples and 3 oranges to get 6 apples!

What numbers do I multiply each fraction by?

+

Divide the LCD by each denominator: 18 ÷ 6 = 3 and 18 ÷ 9 = 2. So multiply the first fraction by 3 and the second by 2.

Do I need to simplify my final answer?

+

Yes! Always check if your answer can be simplified. 1518 \frac{15}{18} can be reduced to 56 \frac{5}{6} by dividing both numerator and denominator by 3.

What if the denominators are harder numbers?

+

The process is the same! Find multiples of each denominator until you find the first common one. For larger numbers, you can also use prime factorization to find the LCD more efficiently.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations